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Abstract
The representation of the resolvent of the one-dimensional Schrodinger operator with a reflectionless potential does not contain the integral term. It is obtained via Jost function simple poles decomposition within the formula for the Green function. As a corollary we have a new expression for the reflectionless potential with a free parameter. The results allow the Green functions for a wide class of multidimensional differential equations with a coefficient proportional to the potential to be obtained. Examples for diffusion and wave equations are given.
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